In order to detect the direction from which plane waves are arriving, it is common to use an array of microphones, or other sensors, which are uniformly spaced along a line, over a plane, or through a region of space. the outputs of the microphones are added together and averaged. Such an array is simple in concept but wasteful of microphones because a particular spacing between two microphones need only occur once if suitable processing is used. A uniform array in which some microphones have been removed is termed a sparse array; such an array requires longer averaging times if it is to achieve similar performance to the equivalent nonsparse array. This paper addresses the question of how to design such arrays when the original filled array consisted of microphones uniformly distributed along a line, over a square or throughout a cubic region of space. the line array has been studied extensively already, and it is found that the cubic array presents a similar, but more difficult problem. the most useful way, in general, of constructing a cubic array is as a product of sparse line arrays, but this does not always give the best answer. The square array is similar to the cubic one, but has an additional type of solution which is very simple and often the most efficient.